Bengaluru, India to Melbourne is an approximately 16.5-hour flight. You'll lose 4 hours traveling from Bengaluru to Melbourne due to the time zone difference. In January, daytime highs in Melbourne are 32°C, while nighttime lows are 17°C. Finish up your sightseeing early on the 14th (Mon) so you can travel to Sydney.

Fly from Melbourne to Sydney in 3.5 hours. Alternatively, you can do a combination of flight and train; or drive. Traveling from Melbourne in January, expect somewhat warmer with lows of 23°C in Sydney. On the 19th (Sat), wrap the sightseeing up by early afternoon so you can travel back home.